Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(518,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.518");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 518.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.518 |
Dual form | 825.2.k.c.782.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70711 | − | 1.70711i | −1.20711 | − | 1.20711i | −0.971960 | − | 0.235147i | \(-0.924443\pi\) |
−0.235147 | − | 0.971960i | \(-0.575557\pi\) | |||||||
\(3\) | 1.41421 | + | 1.00000i | 0.816497 | + | 0.577350i | ||||
\(4\) | 3.82843i | 1.91421i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.707107 | − | 4.12132i | −0.288675 | − | 1.68252i | ||||
\(7\) | 0.585786 | − | 0.585786i | 0.221406 | − | 0.221406i | −0.587684 | − | 0.809091i | \(-0.699960\pi\) |
0.809091 | + | 0.587684i | \(0.199960\pi\) | |||||||
\(8\) | 3.12132 | − | 3.12132i | 1.10355 | − | 1.10355i | ||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | −3.82843 | + | 5.41421i | −1.10517 | + | 1.56295i | ||||
\(13\) | 2.00000 | + | 2.00000i | 0.554700 | + | 0.554700i | 0.927794 | − | 0.373094i | \(-0.121703\pi\) |
−0.373094 | + | 0.927794i | \(0.621703\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 2.82843 | + | 2.82843i | 0.685994 | + | 0.685994i | 0.961344 | − | 0.275350i | \(-0.0887937\pi\) |
−0.275350 | + | 0.961344i | \(0.588794\pi\) | |||||||
\(18\) | 3.12132 | − | 6.53553i | 0.735702 | − | 1.54044i | ||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | − | 0.242641i | 0.308607 | − | 0.0529485i | ||||
\(22\) | −1.70711 | + | 1.70711i | −0.363956 | + | 0.363956i | ||||
\(23\) | −5.24264 | + | 5.24264i | −1.09317 | + | 1.09317i | −0.0979775 | + | 0.995189i | \(0.531237\pi\) |
−0.995189 | + | 0.0979775i | \(0.968763\pi\) | |||||||
\(24\) | 7.53553 | − | 1.29289i | 1.53818 | − | 0.263911i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 6.82843i | − | 1.33916i | ||||||
\(27\) | −1.41421 | + | 5.00000i | −0.272166 | + | 0.962250i | ||||
\(28\) | 2.24264 | + | 2.24264i | 0.423819 | + | 0.423819i | ||||
\(29\) | 4.82843 | 0.896616 | 0.448308 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448308 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.82843 | −1.58563 | −0.792816 | − | 0.609461i | \(-0.791386\pi\) | ||||
−0.792816 | + | 0.609461i | \(0.791386\pi\) | |||||||
\(32\) | −1.12132 | − | 1.12132i | −0.198223 | − | 0.198223i | ||||
\(33\) | 1.00000 | − | 1.41421i | 0.174078 | − | 0.246183i | ||||
\(34\) | − | 9.65685i | − | 1.65614i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.8284 | + | 3.82843i | −1.80474 | + | 0.638071i | ||||
\(37\) | 5.82843 | − | 5.82843i | 0.958188 | − | 0.958188i | −0.0409727 | − | 0.999160i | \(-0.513046\pi\) |
0.999160 | + | 0.0409727i | \(0.0130457\pi\) | |||||||
\(38\) | −4.82843 | + | 4.82843i | −0.783274 | + | 0.783274i | ||||
\(39\) | 0.828427 | + | 4.82843i | 0.132655 | + | 0.773167i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65685i | 0.571105i | 0.958363 | + | 0.285552i | \(0.0921770\pi\) | ||||
−0.958363 | + | 0.285552i | \(0.907823\pi\) | |||||||
\(42\) | −2.82843 | − | 2.00000i | −0.436436 | − | 0.308607i | ||||
\(43\) | 8.24264 | + | 8.24264i | 1.25699 | + | 1.25699i | 0.952522 | + | 0.304469i | \(0.0984788\pi\) |
0.304469 | + | 0.952522i | \(0.401521\pi\) | |||||||
\(44\) | 3.82843 | 0.577157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.8995 | 2.63914 | ||||||||
\(47\) | 1.24264 | + | 1.24264i | 0.181258 | + | 0.181258i | 0.791904 | − | 0.610646i | \(-0.209090\pi\) |
−0.610646 | + | 0.791904i | \(0.709090\pi\) | |||||||
\(48\) | −4.24264 | − | 3.00000i | −0.612372 | − | 0.433013i | ||||
\(49\) | 6.31371i | 0.901958i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17157 | + | 6.82843i | 0.164053 | + | 0.956171i | ||||
\(52\) | −7.65685 | + | 7.65685i | −1.06181 | + | 1.06181i | ||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | 10.9497 | − | 6.12132i | 1.49007 | − | 0.833006i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 3.65685i | − | 0.488668i | ||||||
\(57\) | 2.82843 | − | 4.00000i | 0.374634 | − | 0.529813i | ||||
\(58\) | −8.24264 | − | 8.24264i | −1.08231 | − | 1.08231i | ||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4853 | 1.34250 | 0.671251 | − | 0.741230i | \(-0.265757\pi\) | ||||
0.671251 | + | 0.741230i | \(0.265757\pi\) | |||||||
\(62\) | 15.0711 | + | 15.0711i | 1.91403 | + | 1.91403i | ||||
\(63\) | 2.24264 | + | 1.07107i | 0.282546 | + | 0.134942i | ||||
\(64\) | 9.82843i | 1.22855i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.12132 | + | 0.707107i | −0.507299 | + | 0.0870388i | ||||
\(67\) | 3.58579 | − | 3.58579i | 0.438074 | − | 0.438074i | −0.453290 | − | 0.891363i | \(-0.649750\pi\) |
0.891363 | + | 0.453290i | \(0.149750\pi\) | |||||||
\(68\) | −10.8284 | + | 10.8284i | −1.31314 | + | 1.31314i | ||||
\(69\) | −12.6569 | + | 2.17157i | −1.52371 | + | 0.261427i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4853i | 1.71909i | 0.511063 | + | 0.859543i | \(0.329252\pi\) | ||||
−0.511063 | + | 0.859543i | \(0.670748\pi\) | |||||||
\(72\) | 11.9497 | + | 5.70711i | 1.40829 | + | 0.672589i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | −19.8995 | −2.31327 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.8284 | 1.24211 | ||||||||
\(77\) | −0.585786 | − | 0.585786i | −0.0667566 | − | 0.0667566i | ||||
\(78\) | 6.82843 | − | 9.65685i | 0.773167 | − | 1.09342i | ||||
\(79\) | − | 5.17157i | − | 0.581847i | −0.956746 | − | 0.290924i | \(-0.906037\pi\) | ||
0.956746 | − | 0.290924i | \(-0.0939626\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 6.24264 | − | 6.24264i | 0.689384 | − | 0.689384i | ||||
\(83\) | 5.07107 | − | 5.07107i | 0.556622 | − | 0.556622i | −0.371722 | − | 0.928344i | \(-0.621233\pi\) |
0.928344 | + | 0.371722i | \(0.121233\pi\) | |||||||
\(84\) | 0.928932 | + | 5.41421i | 0.101355 | + | 0.590739i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 28.1421i | − | 3.03464i | ||||||
\(87\) | 6.82843 | + | 4.82843i | 0.732084 | + | 0.517662i | ||||
\(88\) | −3.12132 | − | 3.12132i | −0.332734 | − | 0.332734i | ||||
\(89\) | −1.65685 | −0.175626 | −0.0878131 | − | 0.996137i | \(-0.527988\pi\) | ||||
−0.0878131 | + | 0.996137i | \(0.527988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.34315 | 0.245628 | ||||||||
\(92\) | −20.0711 | − | 20.0711i | −2.09255 | − | 2.09255i | ||||
\(93\) | −12.4853 | − | 8.82843i | −1.29466 | − | 0.915465i | ||||
\(94\) | − | 4.24264i | − | 0.437595i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.464466 | − | 2.70711i | −0.0474044 | − | 0.276293i | ||||
\(97\) | 0.656854 | − | 0.656854i | 0.0666934 | − | 0.0666934i | −0.672973 | − | 0.739667i | \(-0.734983\pi\) |
0.739667 | + | 0.672973i | \(0.234983\pi\) | |||||||
\(98\) | 10.7782 | − | 10.7782i | 1.08876 | − | 1.08876i | ||||
\(99\) | 2.82843 | − | 1.00000i | 0.284268 | − | 0.100504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.8284i | − | 1.27648i | −0.769839 | − | 0.638238i | \(-0.779664\pi\) | ||
0.769839 | − | 0.638238i | \(-0.220336\pi\) | |||||||
\(102\) | 9.65685 | − | 13.6569i | 0.956171 | − | 1.35223i | ||||
\(103\) | 3.58579 | + | 3.58579i | 0.353318 | + | 0.353318i | 0.861343 | − | 0.508025i | \(-0.169624\pi\) |
−0.508025 | + | 0.861343i | \(0.669624\pi\) | |||||||
\(104\) | 12.4853 | 1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.41421 | −0.331618 | ||||||||
\(107\) | −8.24264 | − | 8.24264i | −0.796846 | − | 0.796846i | 0.185751 | − | 0.982597i | \(-0.440528\pi\) |
−0.982597 | + | 0.185751i | \(0.940528\pi\) | |||||||
\(108\) | −19.1421 | − | 5.41421i | −1.84195 | − | 0.520983i | ||||
\(109\) | − | 8.82843i | − | 0.845610i | −0.906221 | − | 0.422805i | \(-0.861046\pi\) | ||
0.906221 | − | 0.422805i | \(-0.138954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0711 | − | 2.41421i | 1.33557 | − | 0.229147i | ||||
\(112\) | −1.75736 | + | 1.75736i | −0.166055 | + | 0.166055i | ||||
\(113\) | −0.171573 | + | 0.171573i | −0.0161402 | + | 0.0161402i | −0.715131 | − | 0.698991i | \(-0.753633\pi\) |
0.698991 | + | 0.715131i | \(0.253633\pi\) | |||||||
\(114\) | −11.6569 | + | 2.00000i | −1.09176 | + | 0.187317i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 18.4853i | 1.71632i | ||||||||
\(117\) | −3.65685 | + | 7.65685i | −0.338076 | + | 0.707876i | ||||
\(118\) | −6.82843 | − | 6.82843i | −0.628608 | − | 0.628608i | ||||
\(119\) | 3.31371 | 0.303767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −17.8995 | − | 17.8995i | −1.62054 | − | 1.62054i | ||||
\(123\) | −3.65685 | + | 5.17157i | −0.329727 | + | 0.466305i | ||||
\(124\) | − | 33.7990i | − | 3.03524i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | − | 5.65685i | −0.178174 | − | 0.503953i | ||||
\(127\) | 1.41421 | − | 1.41421i | 0.125491 | − | 0.125491i | −0.641572 | − | 0.767063i | \(-0.721717\pi\) |
0.767063 | + | 0.641572i | \(0.221717\pi\) | |||||||
\(128\) | 14.5355 | − | 14.5355i | 1.28477 | − | 1.28477i | ||||
\(129\) | 3.41421 | + | 19.8995i | 0.300605 | + | 1.75205i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.17157i | 0.102361i | 0.998689 | + | 0.0511804i | \(0.0162983\pi\) | ||||
−0.998689 | + | 0.0511804i | \(0.983702\pi\) | |||||||
\(132\) | 5.41421 | + | 3.82843i | 0.471247 | + | 0.333222i | ||||
\(133\) | −1.65685 | − | 1.65685i | −0.143667 | − | 0.143667i | ||||
\(134\) | −12.2426 | −1.05760 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.6569 | 1.51406 | ||||||||
\(137\) | 5.82843 | + | 5.82843i | 0.497956 | + | 0.497956i | 0.910801 | − | 0.412845i | \(-0.135465\pi\) |
−0.412845 | + | 0.910801i | \(0.635465\pi\) | |||||||
\(138\) | 25.3137 | + | 17.8995i | 2.15485 | + | 1.52371i | ||||
\(139\) | 6.34315i | 0.538019i | 0.963138 | + | 0.269009i | \(0.0866962\pi\) | ||||
−0.963138 | + | 0.269009i | \(0.913304\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.514719 | + | 3.00000i | 0.0433471 | + | 0.252646i | ||||
\(142\) | 24.7279 | − | 24.7279i | 2.07512 | − | 2.07512i | ||||
\(143\) | 2.00000 | − | 2.00000i | 0.167248 | − | 0.167248i | ||||
\(144\) | −3.00000 | − | 8.48528i | −0.250000 | − | 0.707107i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.31371 | + | 8.92893i | −0.520746 | + | 0.736446i | ||||
\(148\) | 22.3137 | + | 22.3137i | 1.83418 | + | 1.83418i | ||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1421 | −1.47639 | −0.738193 | − | 0.674590i | \(-0.764321\pi\) | ||||
−0.738193 | + | 0.674590i | \(0.764321\pi\) | |||||||
\(152\) | −8.82843 | − | 8.82843i | −0.716080 | − | 0.716080i | ||||
\(153\) | −5.17157 | + | 10.8284i | −0.418097 | + | 0.875426i | ||||
\(154\) | 2.00000i | 0.161165i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −18.4853 | + | 3.17157i | −1.48001 | + | 0.253929i | ||||
\(157\) | −7.48528 | + | 7.48528i | −0.597390 | + | 0.597390i | −0.939617 | − | 0.342227i | \(-0.888819\pi\) |
0.342227 | + | 0.939617i | \(0.388819\pi\) | |||||||
\(158\) | −8.82843 | + | 8.82843i | −0.702352 | + | 0.702352i | ||||
\(159\) | 2.41421 | − | 0.414214i | 0.191460 | − | 0.0328493i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.14214i | 0.484068i | ||||||||
\(162\) | 21.6066 | + | 2.29289i | 1.69757 | + | 0.180147i | ||||
\(163\) | −6.41421 | − | 6.41421i | −0.502400 | − | 0.502400i | 0.409783 | − | 0.912183i | \(-0.365604\pi\) |
−0.912183 | + | 0.409783i | \(0.865604\pi\) | |||||||
\(164\) | −14.0000 | −1.09322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.3137 | −1.34380 | ||||||||
\(167\) | −10.7279 | − | 10.7279i | −0.830152 | − | 0.830152i | 0.157386 | − | 0.987537i | \(-0.449693\pi\) |
−0.987537 | + | 0.157386i | \(0.949693\pi\) | |||||||
\(168\) | 3.65685 | − | 5.17157i | 0.282132 | − | 0.398996i | ||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | − | 2.82843i | 0.611775 | − | 0.216295i | ||||
\(172\) | −31.5563 | + | 31.5563i | −2.40615 | + | 2.40615i | ||||
\(173\) | −8.48528 | + | 8.48528i | −0.645124 | + | 0.645124i | −0.951811 | − | 0.306687i | \(-0.900780\pi\) |
0.306687 | + | 0.951811i | \(0.400780\pi\) | |||||||
\(174\) | −3.41421 | − | 19.8995i | −0.258831 | − | 1.50858i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | 5.65685 | + | 4.00000i | 0.425195 | + | 0.300658i | ||||
\(178\) | 2.82843 | + | 2.82843i | 0.212000 | + | 0.212000i | ||||
\(179\) | 4.14214 | 0.309598 | 0.154799 | − | 0.987946i | \(-0.450527\pi\) | ||||
0.154799 | + | 0.987946i | \(0.450527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.65685 | −0.420471 | −0.210235 | − | 0.977651i | \(-0.567423\pi\) | ||||
−0.210235 | + | 0.977651i | \(0.567423\pi\) | |||||||
\(182\) | −4.00000 | − | 4.00000i | −0.296500 | − | 0.296500i | ||||
\(183\) | 14.8284 | + | 10.4853i | 1.09615 | + | 0.775094i | ||||
\(184\) | 32.7279i | 2.41273i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.24264 | + | 36.3848i | 0.457733 | + | 2.66786i | ||||
\(187\) | 2.82843 | − | 2.82843i | 0.206835 | − | 0.206835i | ||||
\(188\) | −4.75736 | + | 4.75736i | −0.346966 | + | 0.346966i | ||||
\(189\) | 2.10051 | + | 3.75736i | 0.152789 | + | 0.273308i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.3137i | − | 0.818631i | −0.912393 | − | 0.409316i | \(-0.865768\pi\) | ||
0.912393 | − | 0.409316i | \(-0.134232\pi\) | |||||||
\(192\) | −9.82843 | + | 13.8995i | −0.709306 | + | 1.00311i | ||||
\(193\) | −8.00000 | − | 8.00000i | −0.575853 | − | 0.575853i | 0.357905 | − | 0.933758i | \(-0.383491\pi\) |
−0.933758 | + | 0.357905i | \(0.883491\pi\) | |||||||
\(194\) | −2.24264 | −0.161012 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.1716 | −1.72654 | ||||||||
\(197\) | 14.1421 | + | 14.1421i | 1.00759 | + | 1.00759i | 0.999971 | + | 0.00761443i | \(0.00242377\pi\) |
0.00761443 | + | 0.999971i | \(0.497576\pi\) | |||||||
\(198\) | −6.53553 | − | 3.12132i | −0.464460 | − | 0.221823i | ||||
\(199\) | − | 2.48528i | − | 0.176177i | −0.996113 | − | 0.0880885i | \(-0.971924\pi\) | ||
0.996113 | − | 0.0880885i | \(-0.0280758\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.65685 | − | 1.48528i | 0.610607 | − | 0.104764i | ||||
\(202\) | −21.8995 | + | 21.8995i | −1.54084 | + | 1.54084i | ||||
\(203\) | 2.82843 | − | 2.82843i | 0.198517 | − | 0.198517i | ||||
\(204\) | −26.1421 | + | 4.48528i | −1.83032 | + | 0.314033i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 12.2426i | − | 0.852985i | ||||||
\(207\) | −20.0711 | − | 9.58579i | −1.39504 | − | 0.666258i | ||||
\(208\) | −6.00000 | − | 6.00000i | −0.416025 | − | 0.416025i | ||||
\(209\) | −2.82843 | −0.195646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4853 | 0.859522 | 0.429761 | − | 0.902943i | \(-0.358598\pi\) | ||||
0.429761 | + | 0.902943i | \(0.358598\pi\) | |||||||
\(212\) | 3.82843 | + | 3.82843i | 0.262937 | + | 0.262937i | ||||
\(213\) | −14.4853 | + | 20.4853i | −0.992515 | + | 1.40363i | ||||
\(214\) | 28.1421i | 1.92376i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.1924 | + | 20.0208i | 0.761546 | + | 1.36224i | ||||
\(217\) | −5.17157 | + | 5.17157i | −0.351069 | + | 0.351069i | ||||
\(218\) | −15.0711 | + | 15.0711i | −1.02074 | + | 1.02074i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3137i | 0.761042i | ||||||||
\(222\) | −28.1421 | − | 19.8995i | −1.88878 | − | 1.33557i | ||||
\(223\) | −14.5563 | − | 14.5563i | −0.974765 | − | 0.974765i | 0.0249241 | − | 0.999689i | \(-0.492066\pi\) |
−0.999689 | + | 0.0249241i | \(0.992066\pi\) | |||||||
\(224\) | −1.31371 | −0.0877758 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.585786 | 0.0389659 | ||||||||
\(227\) | 1.75736 | + | 1.75736i | 0.116640 | + | 0.116640i | 0.763018 | − | 0.646378i | \(-0.223717\pi\) |
−0.646378 | + | 0.763018i | \(0.723717\pi\) | |||||||
\(228\) | 15.3137 | + | 10.8284i | 1.01418 | + | 0.717130i | ||||
\(229\) | − | 1.65685i | − | 0.109488i | −0.998500 | − | 0.0547440i | \(-0.982566\pi\) | ||
0.998500 | − | 0.0547440i | \(-0.0174343\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.242641 | − | 1.41421i | −0.0159646 | − | 0.0930484i | ||||
\(232\) | 15.0711 | − | 15.0711i | 0.989464 | − | 0.989464i | ||||
\(233\) | 8.34315 | − | 8.34315i | 0.546578 | − | 0.546578i | −0.378872 | − | 0.925449i | \(-0.623688\pi\) |
0.925449 | + | 0.378872i | \(0.123688\pi\) | |||||||
\(234\) | 19.3137 | − | 6.82843i | 1.26258 | − | 0.446388i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.3137i | 0.996838i | ||||||||
\(237\) | 5.17157 | − | 7.31371i | 0.335930 | − | 0.475076i | ||||
\(238\) | −5.65685 | − | 5.65685i | −0.366679 | − | 0.366679i | ||||
\(239\) | −15.7990 | −1.02195 | −0.510976 | − | 0.859595i | \(-0.670716\pi\) | ||||
−0.510976 | + | 0.859595i | \(0.670716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.1421 | −1.81279 | −0.906397 | − | 0.422427i | \(-0.861178\pi\) | ||||
−0.906397 | + | 0.422427i | \(0.861178\pi\) | |||||||
\(242\) | 1.70711 | + | 1.70711i | 0.109737 | + | 0.109737i | ||||
\(243\) | −15.5563 | + | 1.00000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | 40.1421i | 2.56984i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.0711 | − | 2.58579i | 0.960896 | − | 0.164864i | ||||
\(247\) | 5.65685 | − | 5.65685i | 0.359937 | − | 0.359937i | ||||
\(248\) | −27.5563 | + | 27.5563i | −1.74983 | + | 1.74983i | ||||
\(249\) | 12.2426 | − | 2.10051i | 0.775846 | − | 0.133114i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1421i | 0.766405i | 0.923664 | + | 0.383202i | \(0.125179\pi\) | ||||
−0.923664 | + | 0.383202i | \(0.874821\pi\) | |||||||
\(252\) | −4.10051 | + | 8.58579i | −0.258308 | + | 0.540854i | ||||
\(253\) | 5.24264 | + | 5.24264i | 0.329602 | + | 0.329602i | ||||
\(254\) | −4.82843 | −0.302962 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 3.82843 | + | 3.82843i | 0.238811 | + | 0.238811i | 0.816358 | − | 0.577547i | \(-0.195990\pi\) |
−0.577547 | + | 0.816358i | \(0.695990\pi\) | |||||||
\(258\) | 28.1421 | − | 39.7990i | 1.75205 | − | 2.47778i | ||||
\(259\) | − | 6.82843i | − | 0.424298i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.82843 | + | 13.6569i | 0.298872 | + | 0.845338i | ||||
\(262\) | 2.00000 | − | 2.00000i | 0.123560 | − | 0.123560i | ||||
\(263\) | −10.2426 | + | 10.2426i | −0.631588 | + | 0.631588i | −0.948466 | − | 0.316878i | \(-0.897365\pi\) |
0.316878 | + | 0.948466i | \(0.397365\pi\) | |||||||
\(264\) | −1.29289 | − | 7.53553i | −0.0795721 | − | 0.463780i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.65685i | 0.346844i | ||||||||
\(267\) | −2.34315 | − | 1.65685i | −0.143398 | − | 0.101398i | ||||
\(268\) | 13.7279 | + | 13.7279i | 0.838566 | + | 0.838566i | ||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.48528 | −0.515444 | −0.257722 | − | 0.966219i | \(-0.582972\pi\) | ||||
−0.257722 | + | 0.966219i | \(0.582972\pi\) | |||||||
\(272\) | −8.48528 | − | 8.48528i | −0.514496 | − | 0.514496i | ||||
\(273\) | 3.31371 | + | 2.34315i | 0.200555 | + | 0.141814i | ||||
\(274\) | − | 19.8995i | − | 1.20217i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.31371 | − | 48.4558i | −0.500426 | − | 2.91670i | ||||
\(277\) | 1.51472 | − | 1.51472i | 0.0910106 | − | 0.0910106i | −0.660136 | − | 0.751146i | \(-0.729501\pi\) |
0.751146 | + | 0.660136i | \(0.229501\pi\) | |||||||
\(278\) | 10.8284 | − | 10.8284i | 0.649446 | − | 0.649446i | ||||
\(279\) | −8.82843 | − | 24.9706i | −0.528544 | − | 1.49495i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.6274i | − | 0.991909i | −0.868349 | − | 0.495954i | \(-0.834818\pi\) | ||
0.868349 | − | 0.495954i | \(-0.165182\pi\) | |||||||
\(282\) | 4.24264 | − | 6.00000i | 0.252646 | − | 0.357295i | ||||
\(283\) | 0.928932 | + | 0.928932i | 0.0552193 | + | 0.0552193i | 0.734177 | − | 0.678958i | \(-0.237568\pi\) |
−0.678958 | + | 0.734177i | \(0.737568\pi\) | |||||||
\(284\) | −55.4558 | −3.29070 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.82843 | −0.403773 | ||||||||
\(287\) | 2.14214 | + | 2.14214i | 0.126446 | + | 0.126446i | ||||
\(288\) | 2.05025 | − | 4.29289i | 0.120812 | − | 0.252961i | ||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.58579 | − | 0.272078i | 0.0929604 | − | 0.0159495i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.65685 | − | 7.65685i | 0.447318 | − | 0.447318i | −0.447144 | − | 0.894462i | \(-0.647559\pi\) |
0.894462 | + | 0.447144i | \(0.147559\pi\) | |||||||
\(294\) | 26.0208 | − | 4.46447i | 1.51756 | − | 0.260373i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 36.3848i | − | 2.11482i | ||||||
\(297\) | 5.00000 | + | 1.41421i | 0.290129 | + | 0.0820610i | ||||
\(298\) | −17.0711 | − | 17.0711i | −0.988900 | − | 0.988900i | ||||
\(299\) | −20.9706 | −1.21276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.65685 | 0.556612 | ||||||||
\(302\) | 30.9706 | + | 30.9706i | 1.78216 | + | 1.78216i | ||||
\(303\) | 12.8284 | − | 18.1421i | 0.736974 | − | 1.04224i | ||||
\(304\) | 8.48528i | 0.486664i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 27.3137 | − | 9.65685i | 1.56142 | − | 0.552046i | ||||
\(307\) | −7.89949 | + | 7.89949i | −0.450848 | + | 0.450848i | −0.895636 | − | 0.444788i | \(-0.853279\pi\) |
0.444788 | + | 0.895636i | \(0.353279\pi\) | |||||||
\(308\) | 2.24264 | − | 2.24264i | 0.127786 | − | 0.127786i | ||||
\(309\) | 1.48528 | + | 8.65685i | 0.0844947 | + | 0.492471i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.142136i | − | 0.00805977i | −0.999992 | − | 0.00402989i | \(-0.998717\pi\) | ||
0.999992 | − | 0.00402989i | \(-0.00128276\pi\) | |||||||
\(312\) | 17.6569 | + | 12.4853i | 0.999623 | + | 0.706840i | ||||
\(313\) | −1.34315 | − | 1.34315i | −0.0759191 | − | 0.0759191i | 0.668128 | − | 0.744047i | \(-0.267096\pi\) |
−0.744047 | + | 0.668128i | \(0.767096\pi\) | |||||||
\(314\) | 25.5563 | 1.44223 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.7990 | 1.11378 | ||||||||
\(317\) | −20.3137 | − | 20.3137i | −1.14093 | − | 1.14093i | −0.988280 | − | 0.152651i | \(-0.951219\pi\) |
−0.152651 | − | 0.988280i | \(-0.548781\pi\) | |||||||
\(318\) | −4.82843 | − | 3.41421i | −0.270765 | − | 0.191460i | ||||
\(319\) | − | 4.82843i | − | 0.270340i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.41421 | − | 19.8995i | −0.190563 | − | 1.11068i | ||||
\(322\) | 10.4853 | − | 10.4853i | 0.584322 | − | 0.584322i | ||||
\(323\) | 8.00000 | − | 8.00000i | 0.445132 | − | 0.445132i | ||||
\(324\) | −21.6569 | − | 26.7990i | −1.20316 | − | 1.48883i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.8995i | 1.21290i | ||||||||
\(327\) | 8.82843 | − | 12.4853i | 0.488213 | − | 0.690438i | ||||
\(328\) | 11.4142 | + | 11.4142i | 0.630245 | + | 0.630245i | ||||
\(329\) | 1.45584 | 0.0802633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.4853 | 0.576323 | 0.288162 | − | 0.957582i | \(-0.406956\pi\) | ||||
0.288162 | + | 0.957582i | \(0.406956\pi\) | |||||||
\(332\) | 19.4142 | + | 19.4142i | 1.06549 | + | 1.06549i | ||||
\(333\) | 22.3137 | + | 10.6569i | 1.22278 | + | 0.583992i | ||||
\(334\) | 36.6274i | 2.00416i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.24264 | + | 0.727922i | −0.231455 | + | 0.0397114i | ||||
\(337\) | 5.17157 | − | 5.17157i | 0.281714 | − | 0.281714i | −0.552079 | − | 0.833792i | \(-0.686165\pi\) |
0.833792 | + | 0.552079i | \(0.186165\pi\) | |||||||
\(338\) | −8.53553 | + | 8.53553i | −0.464272 | + | 0.464272i | ||||
\(339\) | −0.414214 | + | 0.0710678i | −0.0224970 | + | 0.00385987i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.82843i | 0.478086i | ||||||||
\(342\) | −18.4853 | − | 8.82843i | −0.999570 | − | 0.477387i | ||||
\(343\) | 7.79899 | + | 7.79899i | 0.421106 | + | 0.421106i | ||||
\(344\) | 51.4558 | 2.77431 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.9706 | 1.55747 | ||||||||
\(347\) | −17.8995 | − | 17.8995i | −0.960895 | − | 0.960895i | 0.0383684 | − | 0.999264i | \(-0.487784\pi\) |
−0.999264 | + | 0.0383684i | \(0.987784\pi\) | |||||||
\(348\) | −18.4853 | + | 26.1421i | −0.990915 | + | 1.40137i | ||||
\(349\) | − | 30.0000i | − | 1.60586i | −0.596071 | − | 0.802932i | \(-0.703272\pi\) | ||
0.596071 | − | 0.802932i | \(-0.296728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.8284 | + | 7.17157i | −0.684731 | + | 0.382790i | ||||
\(352\) | −1.12132 | + | 1.12132i | −0.0597666 | + | 0.0597666i | ||||
\(353\) | 2.17157 | − | 2.17157i | 0.115581 | − | 0.115581i | −0.646951 | − | 0.762532i | \(-0.723956\pi\) |
0.762532 | + | 0.646951i | \(0.223956\pi\) | |||||||
\(354\) | −2.82843 | − | 16.4853i | −0.150329 | − | 0.876183i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.34315i | − | 0.336186i | ||||||
\(357\) | 4.68629 | + | 3.31371i | 0.248025 | + | 0.175380i | ||||
\(358\) | −7.07107 | − | 7.07107i | −0.373718 | − | 0.373718i | ||||
\(359\) | −6.14214 | −0.324170 | −0.162085 | − | 0.986777i | \(-0.551822\pi\) | ||||
−0.162085 | + | 0.986777i | \(0.551822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 9.65685 | + | 9.65685i | 0.507553 | + | 0.507553i | ||||
\(363\) | −1.41421 | − | 1.00000i | −0.0742270 | − | 0.0524864i | ||||
\(364\) | 8.97056i | 0.470185i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.41421 | − | 43.2132i | −0.387547 | − | 2.25879i | ||||
\(367\) | 20.8995 | − | 20.8995i | 1.09094 | − | 1.09094i | 0.0955170 | − | 0.995428i | \(-0.469550\pi\) |
0.995428 | − | 0.0955170i | \(-0.0304504\pi\) | |||||||
\(368\) | 15.7279 | − | 15.7279i | 0.819875 | − | 0.819875i | ||||
\(369\) | −10.3431 | + | 3.65685i | −0.538443 | + | 0.190368i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.17157i | − | 0.0608250i | ||||||
\(372\) | 33.7990 | − | 47.7990i | 1.75240 | − | 2.47826i | ||||
\(373\) | −20.4853 | − | 20.4853i | −1.06069 | − | 1.06069i | −0.998035 | − | 0.0626522i | \(-0.980044\pi\) |
−0.0626522 | − | 0.998035i | \(-0.519956\pi\) | |||||||
\(374\) | −9.65685 | −0.499344 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.75736 | 0.400055 | ||||||||
\(377\) | 9.65685 | + | 9.65685i | 0.497353 | + | 0.497353i | ||||
\(378\) | 2.82843 | − | 10.0000i | 0.145479 | − | 0.514344i | ||||
\(379\) | − | 0.142136i | − | 0.00730102i | −0.999993 | − | 0.00365051i | \(-0.998838\pi\) | ||
0.999993 | − | 0.00365051i | \(-0.00116200\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.41421 | − | 0.585786i | 0.174915 | − | 0.0300107i | ||||
\(382\) | −19.3137 | + | 19.3137i | −0.988175 | + | 0.988175i | ||||
\(383\) | 8.07107 | − | 8.07107i | 0.412412 | − | 0.412412i | −0.470166 | − | 0.882578i | \(-0.655806\pi\) |
0.882578 | + | 0.470166i | \(0.155806\pi\) | |||||||
\(384\) | 35.0919 | − | 6.02082i | 1.79078 | − | 0.307248i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.3137i | 1.39023i | ||||||||
\(387\) | −15.0711 | + | 31.5563i | −0.766105 | + | 1.60410i | ||||
\(388\) | 2.51472 | + | 2.51472i | 0.127665 | + | 0.127665i | ||||
\(389\) | −5.31371 | −0.269416 | −0.134708 | − | 0.990885i | \(-0.543010\pi\) | ||||
−0.134708 | + | 0.990885i | \(0.543010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.6569 | −1.49981 | ||||||||
\(392\) | 19.7071 | + | 19.7071i | 0.995359 | + | 0.995359i | ||||
\(393\) | −1.17157 | + | 1.65685i | −0.0590980 | + | 0.0835772i | ||||
\(394\) | − | 48.2843i | − | 2.43253i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.82843 | + | 10.8284i | 0.192386 | + | 0.544149i | ||||
\(397\) | −11.8284 | + | 11.8284i | −0.593652 | + | 0.593652i | −0.938616 | − | 0.344964i | \(-0.887891\pi\) |
0.344964 | + | 0.938616i | \(0.387891\pi\) | |||||||
\(398\) | −4.24264 | + | 4.24264i | −0.212664 | + | 0.212664i | ||||
\(399\) | −0.686292 | − | 4.00000i | −0.0343575 | − | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.3431i | 1.21564i | 0.794075 | + | 0.607819i | \(0.207956\pi\) | ||||
−0.794075 | + | 0.607819i | \(0.792044\pi\) | |||||||
\(402\) | −17.3137 | − | 12.2426i | −0.863529 | − | 0.610607i | ||||
\(403\) | −17.6569 | − | 17.6569i | −0.879551 | − | 0.879551i | ||||
\(404\) | 49.1127 | 2.44345 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.65685 | −0.479262 | ||||||||
\(407\) | −5.82843 | − | 5.82843i | −0.288904 | − | 0.288904i | ||||
\(408\) | 24.9706 | + | 17.6569i | 1.23623 | + | 0.874145i | ||||
\(409\) | − | 1.51472i | − | 0.0748980i | −0.999299 | − | 0.0374490i | \(-0.988077\pi\) | ||
0.999299 | − | 0.0374490i | \(-0.0119232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.41421 | + | 14.0711i | 0.119084 | + | 0.694075i | ||||
\(412\) | −13.7279 | + | 13.7279i | −0.676326 | + | 0.676326i | ||||
\(413\) | 2.34315 | − | 2.34315i | 0.115299 | − | 0.115299i | ||||
\(414\) | 17.8995 | + | 50.6274i | 0.879712 | + | 2.48820i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4.48528i | − | 0.219909i | ||||||
\(417\) | −6.34315 | + | 8.97056i | −0.310625 | + | 0.439290i | ||||
\(418\) | 4.82843 | + | 4.82843i | 0.236166 | + | 0.236166i | ||||
\(419\) | 35.4558 | 1.73213 | 0.866066 | − | 0.499930i | \(-0.166641\pi\) | ||||
0.866066 | + | 0.499930i | \(0.166641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | −21.3137 | − | 21.3137i | −1.03754 | − | 1.03754i | ||||
\(423\) | −2.27208 | + | 4.75736i | −0.110472 | + | 0.231311i | ||||
\(424\) | − | 6.24264i | − | 0.303169i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 59.6985 | − | 10.2426i | 2.89240 | − | 0.496258i | ||||
\(427\) | 6.14214 | − | 6.14214i | 0.297239 | − | 0.297239i | ||||
\(428\) | 31.5563 | − | 31.5563i | 1.52533 | − | 1.52533i | ||||
\(429\) | 4.82843 | − | 0.828427i | 0.233119 | − | 0.0399968i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.6569i | − | 0.850501i | −0.905076 | − | 0.425250i | \(-0.860186\pi\) | ||
0.905076 | − | 0.425250i | \(-0.139814\pi\) | |||||||
\(432\) | 4.24264 | − | 15.0000i | 0.204124 | − | 0.721688i | ||||
\(433\) | −22.3137 | − | 22.3137i | −1.07233 | − | 1.07233i | −0.997172 | − | 0.0751567i | \(-0.976054\pi\) |
−0.0751567 | − | 0.997172i | \(-0.523946\pi\) | |||||||
\(434\) | 17.6569 | 0.847556 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.7990 | 1.61868 | ||||||||
\(437\) | 14.8284 | + | 14.8284i | 0.709340 | + | 0.709340i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3137i | 0.730883i | 0.930834 | + | 0.365442i | \(0.119082\pi\) | ||||
−0.930834 | + | 0.365442i | \(0.880918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.8579 | + | 6.31371i | −0.850374 | + | 0.300653i | ||||
\(442\) | 19.3137 | − | 19.3137i | 0.918659 | − | 0.918659i | ||||
\(443\) | −29.2426 | + | 29.2426i | −1.38936 | + | 1.38936i | −0.562696 | + | 0.826664i | \(0.690236\pi\) |
−0.826664 | + | 0.562696i | \(0.809764\pi\) | |||||||
\(444\) | 9.24264 | + | 53.8701i | 0.438636 | + | 2.55656i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 49.6985i | 2.35329i | ||||||||
\(447\) | 14.1421 | + | 10.0000i | 0.668900 | + | 0.472984i | ||||
\(448\) | 5.75736 | + | 5.75736i | 0.272010 | + | 0.272010i | ||||
\(449\) | 36.9706 | 1.74475 | 0.872374 | − | 0.488838i | \(-0.162579\pi\) | ||||
0.872374 | + | 0.488838i | \(0.162579\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.65685 | 0.172195 | ||||||||
\(452\) | −0.656854 | − | 0.656854i | −0.0308958 | − | 0.0308958i | ||||
\(453\) | −25.6569 | − | 18.1421i | −1.20546 | − | 0.852392i | ||||
\(454\) | − | 6.00000i | − | 0.281594i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.65685 | − | 21.3137i | −0.171248 | − | 0.998106i | ||||
\(457\) | −10.4853 | + | 10.4853i | −0.490481 | + | 0.490481i | −0.908458 | − | 0.417977i | \(-0.862739\pi\) |
0.417977 | + | 0.908458i | \(0.362739\pi\) | |||||||
\(458\) | −2.82843 | + | 2.82843i | −0.132164 | + | 0.132164i | ||||
\(459\) | −18.1421 | + | 10.1421i | −0.846802 | + | 0.473394i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 30.4853i | − | 1.41984i | −0.704282 | − | 0.709921i | \(-0.748731\pi\) | ||
0.704282 | − | 0.709921i | \(-0.251269\pi\) | |||||||
\(462\) | −2.00000 | + | 2.82843i | −0.0930484 | + | 0.131590i | ||||
\(463\) | 13.7279 | + | 13.7279i | 0.637991 | + | 0.637991i | 0.950059 | − | 0.312069i | \(-0.101022\pi\) |
−0.312069 | + | 0.950059i | \(0.601022\pi\) | |||||||
\(464\) | −14.4853 | −0.672462 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.4853 | −1.31956 | ||||||||
\(467\) | 2.41421 | + | 2.41421i | 0.111716 | + | 0.111716i | 0.760755 | − | 0.649039i | \(-0.224829\pi\) |
−0.649039 | + | 0.760755i | \(0.724829\pi\) | |||||||
\(468\) | −29.3137 | − | 14.0000i | −1.35503 | − | 0.647150i | ||||
\(469\) | − | 4.20101i | − | 0.193985i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0711 | + | 3.10051i | −0.832671 | + | 0.142864i | ||||
\(472\) | 12.4853 | − | 12.4853i | 0.574682 | − | 0.574682i | ||||
\(473\) | 8.24264 | − | 8.24264i | 0.378997 | − | 0.378997i | ||||
\(474\) | −21.3137 | + | 3.65685i | −0.978971 | + | 0.167965i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.6863i | 0.581475i | ||||||||
\(477\) | 3.82843 | + | 1.82843i | 0.175292 | + | 0.0837179i | ||||
\(478\) | 26.9706 | + | 26.9706i | 1.23360 | + | 1.23360i | ||||
\(479\) | 1.85786 | 0.0848880 | 0.0424440 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424440 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.3137 | 1.06301 | ||||||||
\(482\) | 48.0416 | + | 48.0416i | 2.18824 | + | 2.18824i | ||||
\(483\) | −6.14214 | + | 8.68629i | −0.279477 | + | 0.395240i | ||||
\(484\) | − | 3.82843i | − | 0.174019i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 28.2635 | + | 24.8492i | 1.28206 | + | 1.12718i | ||||
\(487\) | 13.7279 | − | 13.7279i | 0.622072 | − | 0.622072i | −0.323989 | − | 0.946061i | \(-0.605024\pi\) |
0.946061 | + | 0.323989i | \(0.105024\pi\) | |||||||
\(488\) | 32.7279 | − | 32.7279i | 1.48152 | − | 1.48152i | ||||
\(489\) | −2.65685 | − | 15.4853i | −0.120147 | − | 0.700269i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.0000i | − | 0.902587i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) | ||
0.892375 | − | 0.451294i | \(-0.149037\pi\) | |||||||
\(492\) | −19.7990 | − | 14.0000i | −0.892607 | − | 0.631169i | ||||
\(493\) | 13.6569 | + | 13.6569i | 0.615074 | + | 0.615074i | ||||
\(494\) | −19.3137 | −0.868965 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.4853 | 1.18922 | ||||||||
\(497\) | 8.48528 | + | 8.48528i | 0.380617 | + | 0.380617i | ||||
\(498\) | −24.4853 | − | 17.3137i | −1.09721 | − | 0.775846i | ||||
\(499\) | 19.1716i | 0.858237i | 0.903248 | + | 0.429119i | \(0.141176\pi\) | ||||
−0.903248 | + | 0.429119i | \(0.858824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.44365 | − | 25.8995i | −0.198528 | − | 1.15710i | ||||
\(502\) | 20.7279 | − | 20.7279i | 0.925132 | − | 0.925132i | ||||
\(503\) | 15.0711 | − | 15.0711i | 0.671986 | − | 0.671986i | −0.286188 | − | 0.958174i | \(-0.592388\pi\) |
0.958174 | + | 0.286188i | \(0.0923881\pi\) | |||||||
\(504\) | 10.3431 | − | 3.65685i | 0.460720 | − | 0.162889i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 17.8995i | − | 0.795730i | ||||||
\(507\) | 5.00000 | − | 7.07107i | 0.222058 | − | 0.314037i | ||||
\(508\) | 5.41421 | + | 5.41421i | 0.240217 | + | 0.240217i | ||||
\(509\) | −24.3431 | −1.07899 | −0.539495 | − | 0.841988i | \(-0.681385\pi\) | ||||
−0.539495 | + | 0.841988i | \(0.681385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.0919 | + | 22.0919i | 0.976333 | + | 0.976333i | ||||
\(513\) | 14.1421 | + | 4.00000i | 0.624391 | + | 0.176604i | ||||
\(514\) | − | 13.0711i | − | 0.576540i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −76.1838 | + | 13.0711i | −3.35380 | + | 0.575422i | ||||
\(517\) | 1.24264 | − | 1.24264i | 0.0546513 | − | 0.0546513i | ||||
\(518\) | −11.6569 | + | 11.6569i | −0.512173 | + | 0.512173i | ||||
\(519\) | −20.4853 | + | 3.51472i | −0.899204 | + | 0.154279i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.3431i | − | 0.716006i | −0.933720 | − | 0.358003i | \(-0.883458\pi\) | ||
0.933720 | − | 0.358003i | \(-0.116542\pi\) | |||||||
\(522\) | 15.0711 | − | 31.5563i | 0.659643 | − | 1.38118i | ||||
\(523\) | −15.2132 | − | 15.2132i | −0.665227 | − | 0.665227i | 0.291380 | − | 0.956607i | \(-0.405885\pi\) |
−0.956607 | + | 0.291380i | \(0.905885\pi\) | |||||||
\(524\) | −4.48528 | −0.195940 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.9706 | 1.52479 | ||||||||
\(527\) | −24.9706 | − | 24.9706i | −1.08773 | − | 1.08773i | ||||
\(528\) | −3.00000 | + | 4.24264i | −0.130558 | + | 0.184637i | ||||
\(529\) | − | 31.9706i | − | 1.39002i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | + | 11.3137i | 0.173585 | + | 0.490973i | ||||
\(532\) | 6.34315 | − | 6.34315i | 0.275010 | − | 0.275010i | ||||
\(533\) | −7.31371 | + | 7.31371i | −0.316792 | + | 0.316792i | ||||
\(534\) | 1.17157 | + | 6.82843i | 0.0506989 | + | 0.295495i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 22.3848i | − | 0.966875i | ||||||
\(537\) | 5.85786 | + | 4.14214i | 0.252786 | + | 0.178746i | ||||
\(538\) | −23.8995 | − | 23.8995i | −1.03038 | − | 1.03038i | ||||
\(539\) | 6.31371 | 0.271951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.3137 | −1.43227 | −0.716134 | − | 0.697963i | \(-0.754090\pi\) | ||||
−0.716134 | + | 0.697963i | \(0.754090\pi\) | |||||||
\(542\) | 14.4853 | + | 14.4853i | 0.622196 | + | 0.622196i | ||||
\(543\) | −8.00000 | − | 5.65685i | −0.343313 | − | 0.242759i | ||||
\(544\) | − | 6.34315i | − | 0.271960i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.65685 | − | 9.65685i | −0.0709068 | − | 0.413275i | ||||
\(547\) | −21.8995 | + | 21.8995i | −0.936355 | + | 0.936355i | −0.998092 | − | 0.0617376i | \(-0.980336\pi\) |
0.0617376 | + | 0.998092i | \(0.480336\pi\) | |||||||
\(548\) | −22.3137 | + | 22.3137i | −0.953194 | + | 0.953194i | ||||
\(549\) | 10.4853 | + | 29.6569i | 0.447501 | + | 1.26572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.6569i | − | 0.581802i | ||||||
\(552\) | −32.7279 | + | 46.2843i | −1.39299 | + | 1.96999i | ||||
\(553\) | −3.02944 | − | 3.02944i | −0.128825 | − | 0.128825i | ||||
\(554\) | −5.17157 | −0.219719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.2843 | −1.02988 | ||||||||
\(557\) | −24.9706 | − | 24.9706i | −1.05804 | − | 1.05804i | −0.998209 | − | 0.0598280i | \(-0.980945\pi\) |
−0.0598280 | − | 0.998209i | \(-0.519055\pi\) | |||||||
\(558\) | −27.5563 | + | 57.6985i | −1.16655 | + | 2.44257i | ||||
\(559\) | 32.9706i | 1.39451i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.82843 | − | 1.17157i | 0.288296 | − | 0.0494638i | ||||
\(562\) | −28.3848 | + | 28.3848i | −1.19734 | + | 1.19734i | ||||
\(563\) | 9.89949 | − | 9.89949i | 0.417214 | − | 0.417214i | −0.467028 | − | 0.884242i | \(-0.654675\pi\) |
0.884242 | + | 0.467028i | \(0.154675\pi\) | |||||||
\(564\) | −11.4853 | + | 1.97056i | −0.483618 | + | 0.0829757i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 3.17157i | − | 0.133311i | ||||||
\(567\) | −0.786797 | + | 7.41421i | −0.0330423 | + | 0.311368i | ||||
\(568\) | 45.2132 | + | 45.2132i | 1.89710 | + | 1.89710i | ||||
\(569\) | 39.6569 | 1.66250 | 0.831251 | − | 0.555897i | \(-0.187625\pi\) | ||||
0.831251 | + | 0.555897i | \(0.187625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3431 | 0.767637 | 0.383818 | − | 0.923409i | \(-0.374609\pi\) | ||||
0.383818 | + | 0.923409i | \(0.374609\pi\) | |||||||
\(572\) | 7.65685 | + | 7.65685i | 0.320149 | + | 0.320149i | ||||
\(573\) | 11.3137 | − | 16.0000i | 0.472637 | − | 0.668410i | ||||
\(574\) | − | 7.31371i | − | 0.305268i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −27.7990 | + | 9.82843i | −1.15829 | + | 0.409518i | ||||
\(577\) | −17.0000 | + | 17.0000i | −0.707719 | + | 0.707719i | −0.966055 | − | 0.258336i | \(-0.916826\pi\) |
0.258336 | + | 0.966055i | \(0.416826\pi\) | |||||||
\(578\) | −1.70711 | + | 1.70711i | −0.0710063 | + | 0.0710063i | ||||
\(579\) | −3.31371 | − | 19.3137i | −0.137713 | − | 0.802650i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.94113i | − | 0.246479i | ||||||
\(582\) | −3.17157 | − | 2.24264i | −0.131466 | − | 0.0929604i | ||||
\(583\) | −1.00000 | − | 1.00000i | −0.0414158 | − | 0.0414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.1421 | −1.07992 | ||||||||
\(587\) | 2.41421 | + | 2.41421i | 0.0996453 | + | 0.0996453i | 0.755172 | − | 0.655527i | \(-0.227553\pi\) |
−0.655527 | + | 0.755172i | \(0.727553\pi\) | |||||||
\(588\) | −34.1838 | − | 24.1716i | −1.40971 | − | 0.996819i | ||||
\(589\) | 24.9706i | 1.02889i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.85786 | + | 34.1421i | 0.240960 | + | 1.40442i | ||||
\(592\) | −17.4853 | + | 17.4853i | −0.718641 | + | 0.718641i | ||||
\(593\) | 34.1421 | − | 34.1421i | 1.40205 | − | 1.40205i | 0.608481 | − | 0.793568i | \(-0.291779\pi\) |
0.793568 | − | 0.608481i | \(-0.208221\pi\) | |||||||
\(594\) | −6.12132 | − | 10.9497i | −0.251161 | − | 0.449274i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 38.2843i | 1.56818i | ||||||||
\(597\) | 2.48528 | − | 3.51472i | 0.101716 | − | 0.143848i | ||||
\(598\) | 35.7990 | + | 35.7990i | 1.46393 | + | 1.46393i | ||||
\(599\) | −47.4558 | −1.93899 | −0.969497 | − | 0.245105i | \(-0.921178\pi\) | ||||
−0.969497 | + | 0.245105i | \(0.921178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.4558 | 0.956784 | 0.478392 | − | 0.878146i | \(-0.341220\pi\) | ||||
0.478392 | + | 0.878146i | \(0.341220\pi\) | |||||||
\(602\) | −16.4853 | − | 16.4853i | −0.671890 | − | 0.671890i | ||||
\(603\) | 13.7279 | + | 6.55635i | 0.559044 | + | 0.266995i | ||||
\(604\) | − | 69.4558i | − | 2.82612i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −52.8701 | + | 9.07107i | −2.14770 | + | 0.368487i | ||||
\(607\) | 2.10051 | − | 2.10051i | 0.0852569 | − | 0.0852569i | −0.663192 | − | 0.748449i | \(-0.730799\pi\) |
0.748449 | + | 0.663192i | \(0.230799\pi\) | |||||||
\(608\) | −3.17157 | + | 3.17157i | −0.128624 | + | 0.128624i | ||||
\(609\) | 6.82843 | − | 1.17157i | 0.276702 | − | 0.0474745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.97056i | 0.201087i | ||||||||
\(612\) | −41.4558 | − | 19.7990i | −1.67575 | − | 0.800327i | ||||
\(613\) | 16.0000 | + | 16.0000i | 0.646234 | + | 0.646234i | 0.952081 | − | 0.305847i | \(-0.0989395\pi\) |
−0.305847 | + | 0.952081i | \(0.598940\pi\) | |||||||
\(614\) | 26.9706 | 1.08844 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.65685 | −0.147339 | ||||||||
\(617\) | 24.1716 | + | 24.1716i | 0.973111 | + | 0.973111i | 0.999648 | − | 0.0265370i | \(-0.00844797\pi\) |
−0.0265370 | + | 0.999648i | \(0.508448\pi\) | |||||||
\(618\) | 12.2426 | − | 17.3137i | 0.492471 | − | 0.696459i | ||||
\(619\) | − | 23.3137i | − | 0.937057i | −0.883448 | − | 0.468529i | \(-0.844784\pi\) | ||
0.883448 | − | 0.468529i | \(-0.155216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.7990 | − | 33.6274i | −0.754377 | − | 1.34942i | ||||
\(622\) | −0.242641 | + | 0.242641i | −0.00972901 | + | 0.00972901i | ||||
\(623\) | −0.970563 | + | 0.970563i | −0.0388848 | + | 0.0388848i | ||||
\(624\) | −2.48528 | − | 14.4853i | −0.0994909 | − | 0.579875i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.58579i | 0.183285i | ||||||||
\(627\) | −4.00000 | − | 2.82843i | −0.159745 | − | 0.112956i | ||||
\(628\) | −28.6569 | − | 28.6569i | −1.14353 | − | 1.14353i | ||||
\(629\) | 32.9706 | 1.31462 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.9706 | 0.675587 | 0.337794 | − | 0.941220i | \(-0.390319\pi\) | ||||
0.337794 | + | 0.941220i | \(0.390319\pi\) | |||||||
\(632\) | −16.1421 | − | 16.1421i | −0.642100 | − | 0.642100i | ||||
\(633\) | 17.6569 | + | 12.4853i | 0.701797 | + | 0.496245i | ||||
\(634\) | 69.3553i | 2.75445i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.58579 | + | 9.24264i | 0.0628805 | + | 0.366495i | ||||
\(637\) | −12.6274 | + | 12.6274i | −0.500316 | + | 0.500316i | ||||
\(638\) | −8.24264 | + | 8.24264i | −0.326329 | + | 0.326329i | ||||
\(639\) | −40.9706 | + | 14.4853i | −1.62077 | + | 0.573029i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6274i | 0.498753i | 0.968407 | + | 0.249376i | \(0.0802257\pi\) | ||||
−0.968407 | + | 0.249376i | \(0.919774\pi\) | |||||||
\(642\) | −28.1421 | + | 39.7990i | −1.11068 | + | 1.57074i | ||||
\(643\) | 0.757359 | + | 0.757359i | 0.0298673 | + | 0.0298673i | 0.721883 | − | 0.692015i | \(-0.243277\pi\) |
−0.692015 | + | 0.721883i | \(0.743277\pi\) | |||||||
\(644\) | −23.5147 | −0.926610 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.3137 | −1.07464 | ||||||||
\(647\) | −13.7279 | − | 13.7279i | −0.539700 | − | 0.539700i | 0.383741 | − | 0.923441i | \(-0.374636\pi\) |
−0.923441 | + | 0.383741i | \(0.874636\pi\) | |||||||
\(648\) | −4.19239 | + | 39.5061i | −0.164693 | + | 1.55195i | ||||
\(649\) | − | 4.00000i | − | 0.157014i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.4853 | + | 2.14214i | −0.489337 | + | 0.0839569i | ||||
\(652\) | 24.5563 | − | 24.5563i | 0.961701 | − | 0.961701i | ||||
\(653\) | −2.65685 | + | 2.65685i | −0.103971 | + | 0.103971i | −0.757179 | − | 0.653208i | \(-0.773423\pi\) |
0.653208 | + | 0.757179i | \(0.273423\pi\) | |||||||
\(654\) | −36.3848 | + | 6.24264i | −1.42276 | + | 0.244107i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 10.9706i | − | 0.428329i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.48528 | − | 2.48528i | −0.0968864 | − | 0.0968864i | ||||
\(659\) | −8.97056 | −0.349444 | −0.174722 | − | 0.984618i | \(-0.555903\pi\) | ||||
−0.174722 | + | 0.984618i | \(0.555903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | −17.8995 | − | 17.8995i | −0.695684 | − | 0.695684i | ||||
\(663\) | −11.3137 | + | 16.0000i | −0.439388 | + | 0.621389i | ||||
\(664\) | − | 31.6569i | − | 1.22852i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19.8995 | − | 56.2843i | −0.771090 | − | 2.18097i | ||||
\(667\) | −25.3137 | + | 25.3137i | −0.980151 | + | 0.980151i | ||||
\(668\) | 41.0711 | − | 41.0711i | 1.58909 | − | 1.58909i | ||||
\(669\) | −6.02944 | − | 35.1421i | −0.233112 | − | 1.35867i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.4853i | − | 0.404780i | ||||||
\(672\) | −1.85786 | − | 1.31371i | −0.0716687 | − | 0.0506774i | ||||
\(673\) | 33.6569 | + | 33.6569i | 1.29738 | + | 1.29738i | 0.930120 | + | 0.367257i | \(0.119703\pi\) |
0.367257 | + | 0.930120i | \(0.380297\pi\) | |||||||
\(674\) | −17.6569 | −0.680117 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.1421 | 0.736236 | ||||||||
\(677\) | 8.34315 | + | 8.34315i | 0.320653 | + | 0.320653i | 0.849018 | − | 0.528365i | \(-0.177195\pi\) |
−0.528365 | + | 0.849018i | \(0.677195\pi\) | |||||||
\(678\) | 0.828427 | + | 0.585786i | 0.0318156 | + | 0.0224970i | ||||
\(679\) | − | 0.769553i | − | 0.0295327i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.727922 | + | 4.24264i | 0.0278940 | + | 0.162578i | ||||
\(682\) | 15.0711 | − | 15.0711i | 0.577101 | − | 0.577101i | ||||
\(683\) | −17.7279 | + | 17.7279i | −0.678340 | + | 0.678340i | −0.959624 | − | 0.281284i | \(-0.909240\pi\) |
0.281284 | + | 0.959624i | \(0.409240\pi\) | |||||||
\(684\) | 10.8284 | + | 30.6274i | 0.414035 | + | 1.17107i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 26.6274i | − | 1.01664i | ||||||
\(687\) | 1.65685 | − | 2.34315i | 0.0632129 | − | 0.0893966i | ||||
\(688\) | −24.7279 | − | 24.7279i | −0.942743 | − | 0.942743i | ||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −32.4853 | − | 32.4853i | −1.23491 | − | 1.23491i | ||||
\(693\) | 1.07107 | − | 2.24264i | 0.0406865 | − | 0.0851909i | ||||
\(694\) | 61.1127i | 2.31981i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 36.3848 | − | 6.24264i | 1.37916 | − | 0.236627i | ||||
\(697\) | −10.3431 | + | 10.3431i | −0.391775 | + | 0.391775i | ||||
\(698\) | −51.2132 | + | 51.2132i | −1.93845 | + | 1.93845i | ||||
\(699\) | 20.1421 | − | 3.45584i | 0.761846 | − | 0.130712i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.3137i | − | 0.805008i | −0.915418 | − | 0.402504i | \(-0.868140\pi\) | ||
0.915418 | − | 0.402504i | \(-0.131860\pi\) | |||||||
\(702\) | 34.1421 | + | 9.65685i | 1.28861 | + | 0.364474i | ||||
\(703\) | −16.4853 | − | 16.4853i | −0.621754 | − | 0.621754i | ||||
\(704\) | 9.82843 | 0.370423 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.41421 | −0.279038 | ||||||||
\(707\) | −7.51472 | − | 7.51472i | −0.282620 | − | 0.282620i | ||||
\(708\) | −15.3137 | + | 21.6569i | −0.575524 | + | 0.813914i | ||||
\(709\) | 6.68629i | 0.251109i | 0.992087 | + | 0.125554i | \(0.0400710\pi\) | ||||
−0.992087 | + | 0.125554i | \(0.959929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6274 | − | 5.17157i | 0.548571 | − | 0.193949i | ||||
\(712\) | −5.17157 | + | 5.17157i | −0.193813 | + | 0.193813i | ||||
\(713\) | 46.2843 | − | 46.2843i | 1.73336 | − | 1.73336i | ||||
\(714\) | −2.34315 | − | 13.6569i | −0.0876900 | − | 0.511095i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.8579i | 0.592636i | ||||||||
\(717\) | −22.3431 | − | 15.7990i | −0.834420 | − | 0.590024i | ||||
\(718\) | 10.4853 | + | 10.4853i | 0.391307 | + | 0.391307i | ||||
\(719\) | −50.7696 | −1.89338 | −0.946692 | − | 0.322139i | \(-0.895598\pi\) | ||||
−0.946692 | + | 0.322139i | \(0.895598\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.20101 | 0.156454 | ||||||||
\(722\) | −18.7782 | − | 18.7782i | −0.698851 | − | 0.698851i | ||||
\(723\) | −39.7990 | − | 28.1421i | −1.48014 | − | 1.04662i | ||||
\(724\) | − | 21.6569i | − | 0.804871i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.707107 | + | 4.12132i | 0.0262432 | + | 0.152957i | ||||
\(727\) | 22.2132 | − | 22.2132i | 0.823842 | − | 0.823842i | −0.162815 | − | 0.986657i | \(-0.552057\pi\) |
0.986657 | + | 0.162815i | \(0.0520572\pi\) | |||||||
\(728\) | 7.31371 | − | 7.31371i | 0.271064 | − | 0.271064i | ||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.6274i | 1.72458i | ||||||||
\(732\) | −40.1421 | + | 56.7696i | −1.48370 | + | 2.09826i | ||||
\(733\) | 35.7990 | + | 35.7990i | 1.32227 | + | 1.32227i | 0.911938 | + | 0.410328i | \(0.134586\pi\) |
0.410328 | + | 0.911938i | \(0.365414\pi\) | |||||||
\(734\) | −71.3553 | −2.63377 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.7574 | 0.433382 | ||||||||
\(737\) | −3.58579 | − | 3.58579i | −0.132084 | − | 0.132084i | ||||
\(738\) | 23.8995 | + | 11.4142i | 0.879753 | + | 0.420163i | ||||
\(739\) | 30.6274i | 1.12665i | 0.826236 | + | 0.563324i | \(0.190478\pi\) | ||||
−0.826236 | + | 0.563324i | \(0.809522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.6569 | − | 2.34315i | 0.501697 | − | 0.0860776i | ||||
\(742\) | −2.00000 | + | 2.00000i | −0.0734223 | + | 0.0734223i | ||||
\(743\) | 22.0416 | − | 22.0416i | 0.808629 | − | 0.808629i | −0.175797 | − | 0.984426i | \(-0.556250\pi\) |
0.984426 | + | 0.175797i | \(0.0562504\pi\) | |||||||
\(744\) | −66.5269 | + | 11.4142i | −2.43899 | + | 0.418465i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 69.9411i | 2.56073i | ||||||||
\(747\) | 19.4142 | + | 9.27208i | 0.710329 | + | 0.339248i | ||||
\(748\) | 10.8284 | + | 10.8284i | 0.395927 | + | 0.395927i | ||||
\(749\) | −9.65685 | −0.352854 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.37258 | −0.0500863 | −0.0250431 | − | 0.999686i | \(-0.507972\pi\) | ||||
−0.0250431 | + | 0.999686i | \(0.507972\pi\) | |||||||
\(752\) | −3.72792 | − | 3.72792i | −0.135943 | − | 0.135943i | ||||
\(753\) | −12.1421 | + | 17.1716i | −0.442484 | + | 0.625767i | ||||
\(754\) | − | 32.9706i | − | 1.20072i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −14.3848 | + | 8.04163i | −0.523169 | + | 0.292471i | ||||
\(757\) | −5.82843 | + | 5.82843i | −0.211838 | + | 0.211838i | −0.805048 | − | 0.593210i | \(-0.797860\pi\) |
0.593210 | + | 0.805048i | \(0.297860\pi\) | |||||||
\(758\) | −0.242641 | + | 0.242641i | −0.00881311 | + | 0.00881311i | ||||
\(759\) | 2.17157 | + | 12.6569i | 0.0788231 | + | 0.459415i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.4853i | 0.670091i | 0.942202 | + | 0.335045i | \(0.108752\pi\) | ||||
−0.942202 | + | 0.335045i | \(0.891248\pi\) | |||||||
\(762\) | −6.82843 | − | 4.82843i | −0.247368 | − | 0.174915i | ||||
\(763\) | −5.17157 | − | 5.17157i | −0.187224 | − | 0.187224i | ||||
\(764\) | 43.3137 | 1.56703 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.5563 | −0.995651 | ||||||||
\(767\) | 8.00000 | + | 8.00000i | 0.288863 | + | 0.288863i | ||||
\(768\) | −42.3848 | − | 29.9706i | −1.52943 | − | 1.08147i | ||||
\(769\) | 7.37258i | 0.265862i | 0.991125 | + | 0.132931i | \(0.0424389\pi\) | ||||
−0.991125 | + | 0.132931i | \(0.957561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.58579 | + | 9.24264i | 0.0571107 | + | 0.332866i | ||||
\(772\) | 30.6274 | − | 30.6274i | 1.10230 | − | 1.10230i | ||||
\(773\) | −0.656854 | + | 0.656854i | −0.0236254 | + | 0.0236254i | −0.718821 | − | 0.695195i | \(-0.755318\pi\) |
0.695195 | + | 0.718821i | \(0.255318\pi\) | |||||||
\(774\) | 79.5980 | − | 28.1421i | 2.86109 | − | 1.01155i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 4.10051i | − | 0.147200i | ||||||
\(777\) | 6.82843 | − | 9.65685i | 0.244968 | − | 0.346438i | ||||
\(778\) | 9.07107 | + | 9.07107i | 0.325214 | + | 0.325214i | ||||
\(779\) | 10.3431 | 0.370582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4853 | 0.518324 | ||||||||
\(782\) | 50.6274 | + | 50.6274i | 1.81043 | + | 1.81043i | ||||
\(783\) | −6.82843 | + | 24.1421i | −0.244028 | + | 0.862770i | ||||
\(784\) | − | 18.9411i | − | 0.676469i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.82843 | − | 0.828427i | 0.172224 | − | 0.0295490i | ||||
\(787\) | 31.4142 | − | 31.4142i | 1.11980 | − | 1.11980i | 0.128025 | − | 0.991771i | \(-0.459136\pi\) |
0.991771 | − | 0.128025i | \(-0.0408637\pi\) | |||||||
\(788\) | −54.1421 | + | 54.1421i | −1.92873 | + | 1.92873i | ||||
\(789\) | −24.7279 | + | 4.24264i | −0.880337 | + | 0.151042i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.201010i | 0.00714710i | ||||||||
\(792\) | 5.70711 | − | 11.9497i | 0.202793 | − | 0.424616i | ||||
\(793\) | 20.9706 | + | 20.9706i | 0.744687 | + | 0.744687i | ||||
\(794\) | 40.3848 | 1.43320 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.51472 | 0.337240 | ||||||||
\(797\) | −7.97056 | − | 7.97056i | −0.282332 | − | 0.282332i | 0.551707 | − | 0.834038i | \(-0.313977\pi\) |
−0.834038 | + | 0.551707i | \(0.813977\pi\) | |||||||
\(798\) | −5.65685 | + | 8.00000i | −0.200250 | + | 0.283197i | ||||
\(799\) | 7.02944i | 0.248684i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.65685 | − | 4.68629i | −0.0585421 | − | 0.165582i | ||||
\(802\) | 41.5563 | − | 41.5563i | 1.46741 | − | 1.46741i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.68629 | + | 33.1421i | 0.200540 | + | 1.16883i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 60.2843i | 2.12342i | ||||||||
\(807\) | 19.7990 | + | 14.0000i | 0.696957 | + | 0.492823i | ||||
\(808\) | −40.0416 | − | 40.0416i | −1.40866 | − | 1.40866i | ||||
\(809\) | 44.1421 | 1.55195 | 0.775977 | − | 0.630761i | \(-0.217257\pi\) | ||||
0.775977 | + | 0.630761i | \(0.217257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.3431 | −1.06549 | −0.532746 | − | 0.846275i | \(-0.678840\pi\) | ||||
−0.532746 | + | 0.846275i | \(0.678840\pi\) | |||||||
\(812\) | 10.8284 | + | 10.8284i | 0.380003 | + | 0.380003i | ||||
\(813\) | −12.0000 | − | 8.48528i | −0.420858 | − | 0.297592i | ||||
\(814\) | 19.8995i | 0.697477i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.51472 | − | 20.4853i | −0.123040 | − | 0.717128i | ||||
\(817\) | 23.3137 | − | 23.3137i | 0.815643 | − | 0.815643i | ||||
\(818\) | −2.58579 | + | 2.58579i | −0.0904099 | + | 0.0904099i | ||||
\(819\) | 2.34315 | + | 6.62742i | 0.0818761 | + | 0.231581i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 11.6569i | − | 0.406827i | −0.979093 | − | 0.203414i | \(-0.934796\pi\) | ||
0.979093 | − | 0.203414i | \(-0.0652036\pi\) | |||||||
\(822\) | 19.8995 | − | 28.1421i | 0.694075 | − | 0.981570i | ||||
\(823\) | 15.5858 | + | 15.5858i | 0.543286 | + | 0.543286i | 0.924491 | − | 0.381204i | \(-0.124491\pi\) |
−0.381204 | + | 0.924491i | \(0.624491\pi\) | |||||||
\(824\) | 22.3848 | 0.779811 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 20.0416 | + | 20.0416i | 0.696916 | + | 0.696916i | 0.963744 | − | 0.266828i | \(-0.0859757\pi\) |
−0.266828 | + | 0.963744i | \(0.585976\pi\) | |||||||
\(828\) | 36.6985 | − | 76.8406i | 1.27536 | − | 2.67040i | ||||
\(829\) | 22.9706i | 0.797801i | 0.916994 | + | 0.398900i | \(0.130608\pi\) | ||||
−0.916994 | + | 0.398900i | \(0.869392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.65685 | − | 0.627417i | 0.126855 | − | 0.0217649i | ||||
\(832\) | −19.6569 | + | 19.6569i | −0.681479 | + | 0.681479i | ||||
\(833\) | −17.8579 | + | 17.8579i | −0.618738 | + | 0.618738i | ||||
\(834\) | 26.1421 | − | 4.48528i | 0.905228 | − | 0.155313i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 10.8284i | − | 0.374509i | ||||||
\(837\) | 12.4853 | − | 44.1421i | 0.431554 | − | 1.52578i | ||||
\(838\) | −60.5269 | − | 60.5269i | −2.09087 | − | 2.09087i | ||||
\(839\) | 10.3431 | 0.357085 | 0.178543 | − | 0.983932i | \(-0.442862\pi\) | ||||
0.178543 | + | 0.983932i | \(0.442862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 6.82843 | + | 6.82843i | 0.235323 | + | 0.235323i | ||||
\(843\) | 16.6274 | − | 23.5147i | 0.572679 | − | 0.809890i | ||||
\(844\) | 47.7990i | 1.64531i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0000 | − | 4.24264i | 0.412568 | − | 0.145865i | ||||
\(847\) | −0.585786 | + | 0.585786i | −0.0201279 | + | 0.0201279i | ||||
\(848\) | −3.00000 | + | 3.00000i | −0.103020 | + | 0.103020i | ||||
\(849\) | 0.384776 | + | 2.24264i | 0.0132055 | + | 0.0769672i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.1127i | 2.09492i | ||||||||
\(852\) | −78.4264 | − | 55.4558i | −2.68684 | − | 1.89989i | ||||
\(853\) | 10.1421 | + | 10.1421i | 0.347260 | + | 0.347260i | 0.859088 | − | 0.511828i | \(-0.171031\pi\) |
−0.511828 | + | 0.859088i | \(0.671031\pi\) | |||||||
\(854\) | −20.9706 | −0.717598 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −51.4558 | −1.75872 | ||||||||
\(857\) | 0.485281 | + | 0.485281i | 0.0165769 | + | 0.0165769i | 0.715347 | − | 0.698770i | \(-0.246269\pi\) |
−0.698770 | + | 0.715347i | \(0.746269\pi\) | |||||||
\(858\) | −9.65685 | − | 6.82843i | −0.329680 | − | 0.233119i | ||||
\(859\) | − | 36.0000i | − | 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.887302 | + | 5.17157i | 0.0302392 | + | 0.176247i | ||||
\(862\) | −30.1421 | + | 30.1421i | −1.02665 | + | 1.02665i | ||||
\(863\) | −18.5563 | + | 18.5563i | −0.631665 | + | 0.631665i | −0.948486 | − | 0.316820i | \(-0.897385\pi\) |
0.316820 | + | 0.948486i | \(0.397385\pi\) | |||||||
\(864\) | 7.19239 | − | 4.02082i | 0.244690 | − | 0.136791i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 76.1838i | 2.58883i | ||||||||
\(867\) | 1.00000 | − | 1.41421i | 0.0339618 | − | 0.0480292i | ||||
\(868\) | −19.7990 | − | 19.7990i | −0.672022 | − | 0.672022i | ||||
\(869\) | −5.17157 | −0.175434 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3431 | 0.485999 | ||||||||
\(872\) | −27.5563 | − | 27.5563i | −0.933176 | − | 0.933176i | ||||
\(873\) | 2.51472 | + | 1.20101i | 0.0851103 | + | 0.0406480i | ||||
\(874\) | − | 50.6274i | − | 1.71250i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.6274 | − | 38.6274i | 1.30436 | − | 1.30436i | 0.378930 | − | 0.925425i | \(-0.376292\pi\) |
0.925425 | − | 0.378930i | \(-0.123708\pi\) | |||||||
\(878\) | 26.1421 | − | 26.1421i | 0.882254 | − | 0.882254i | ||||
\(879\) | 18.4853 | − | 3.17157i | 0.623493 | − | 0.106974i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.9706i | − | 0.706516i | −0.935526 | − | 0.353258i | \(-0.885074\pi\) | ||
0.935526 | − | 0.353258i | \(-0.114926\pi\) | |||||||
\(882\) | 41.2635 | + | 19.7071i | 1.38941 | + | 0.663573i | ||||
\(883\) | 6.41421 | + | 6.41421i | 0.215855 | + | 0.215855i | 0.806749 | − | 0.590894i | \(-0.201225\pi\) |
−0.590894 | + | 0.806749i | \(0.701225\pi\) | |||||||
\(884\) | −43.3137 | −1.45680 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 99.8406 | 3.35421 | ||||||||
\(887\) | −18.2426 | − | 18.2426i | −0.612528 | − | 0.612528i | 0.331076 | − | 0.943604i | \(-0.392588\pi\) |
−0.943604 | + | 0.331076i | \(0.892588\pi\) | |||||||
\(888\) | 36.3848 | − | 51.4558i | 1.22099 | − | 1.72675i | ||||
\(889\) | − | 1.65685i | − | 0.0555691i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.65685 | + | 7.00000i | 0.189512 | + | 0.234509i | ||||
\(892\) | 55.7279 | − | 55.7279i | 1.86591 | − | 1.86591i | ||||
\(893\) | 3.51472 | − | 3.51472i | 0.117616 | − | 0.117616i | ||||
\(894\) | −7.07107 | − | 41.2132i | −0.236492 | − | 1.37838i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 17.0294i | − | 0.568914i | ||||||
\(897\) | −29.6569 | − | 20.9706i | −0.990214 | − | 0.700187i | ||||
\(898\) | −63.1127 | − | 63.1127i | −2.10610 | − | 2.10610i | ||||
\(899\) | −42.6274 | −1.42170 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.65685 | 0.188457 | ||||||||
\(902\) | −6.24264 | − | 6.24264i | −0.207857 | − | 0.207857i | ||||
\(903\) | 13.6569 | + | 9.65685i | 0.454472 | + | 0.321360i | ||||
\(904\) | 1.07107i | 0.0356232i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.8284 | + | 74.7696i | 0.426196 | + | 2.48405i | ||||
\(907\) | 19.0416 | − | 19.0416i | 0.632267 | − | 0.632267i | −0.316369 | − | 0.948636i | \(-0.602464\pi\) |
0.948636 | + | 0.316369i | \(0.102464\pi\) | |||||||
\(908\) | −6.72792 | + | 6.72792i | −0.223274 | + | 0.223274i | ||||
\(909\) | 36.2843 | − | 12.8284i | 1.20347 | − | 0.425492i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 56.0000i | − | 1.85536i | −0.373373 | − | 0.927681i | \(-0.621799\pi\) | ||
0.373373 | − | 0.927681i | \(-0.378201\pi\) | |||||||
\(912\) | −8.48528 | + | 12.0000i | −0.280976 | + | 0.397360i | ||||
\(913\) | −5.07107 | − | 5.07107i | −0.167828 | − | 0.167828i | ||||
\(914\) | 35.7990 | 1.18413 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.34315 | 0.209583 | ||||||||
\(917\) | 0.686292 | + | 0.686292i | 0.0226633 | + | 0.0226633i | ||||
\(918\) | 48.2843 | + | 13.6569i | 1.59362 | + | 0.450743i | ||||
\(919\) | − | 30.6274i | − | 1.01031i | −0.863030 | − | 0.505153i | \(-0.831436\pi\) | ||
0.863030 | − | 0.505153i | \(-0.168564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.0711 | + | 3.27208i | −0.628413 | + | 0.107819i | ||||
\(922\) | −52.0416 | + | 52.0416i | −1.71390 | + | 1.71390i | ||||
\(923\) | −28.9706 | + | 28.9706i | −0.953578 | + | 0.953578i | ||||
\(924\) | 5.41421 | − | 0.928932i | 0.178115 | − | 0.0305596i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 46.8701i | − | 1.54025i | ||||||
\(927\) | −6.55635 | + | 13.7279i | −0.215339 | + | 0.450884i | ||||
\(928\) | −5.41421 | − | 5.41421i | −0.177730 | − | 0.177730i | ||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.8579 | 0.585268 | ||||||||
\(932\) | 31.9411 | + | 31.9411i | 1.04627 | + | 1.04627i | ||||
\(933\) | 0.142136 | − | 0.201010i | 0.00465331 | − | 0.00658078i | ||||
\(934\) | − | 8.24264i | − | 0.269707i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.4853 | + | 35.3137i | 0.408094 | + | 1.15426i | ||||
\(937\) | −22.9706 | + | 22.9706i | −0.750416 | + | 0.750416i | −0.974557 | − | 0.224141i | \(-0.928042\pi\) |
0.224141 | + | 0.974557i | \(0.428042\pi\) | |||||||
\(938\) | −7.17157 | + | 7.17157i | −0.234160 | + | 0.234160i | ||||
\(939\) | −0.556349 | − | 3.24264i | −0.0181558 | − | 0.105820i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 25.1127i | − | 0.818651i | −0.912389 | − | 0.409325i | \(-0.865764\pi\) | ||
0.912389 | − | 0.409325i | \(-0.134236\pi\) | |||||||
\(942\) | 36.1421 | + | 25.5563i | 1.17757 | + | 0.832671i | ||||
\(943\) | −19.1716 | − | 19.1716i | −0.624312 | − | 0.624312i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.1421 | −0.914980 | ||||||||
\(947\) | −8.75736 | − | 8.75736i | −0.284576 | − | 0.284576i | 0.550355 | − | 0.834931i | \(-0.314492\pi\) |
−0.834931 | + | 0.550355i | \(0.814492\pi\) | |||||||
\(948\) | 28.0000 | + | 19.7990i | 0.909398 | + | 0.643041i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.41421 | − | 49.0416i | −0.272850 | − | 1.59028i | ||||
\(952\) | 10.3431 | − | 10.3431i | 0.335223 | − | 0.335223i | ||||
\(953\) | −33.7990 | + | 33.7990i | −1.09486 | + | 1.09486i | −0.0998546 | + | 0.995002i | \(0.531838\pi\) |
−0.995002 | + | 0.0998546i | \(0.968162\pi\) | |||||||
\(954\) | −3.41421 | − | 9.65685i | −0.110539 | − | 0.312652i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 60.4853i | − | 1.95623i | ||||||
\(957\) | 4.82843 | − | 6.82843i | 0.156081 | − | 0.220732i | ||||
\(958\) | −3.17157 | − | 3.17157i | −0.102469 | − | 0.102469i | ||||
\(959\) | 6.82843 | 0.220501 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | −39.7990 | − | 39.7990i | −1.28317 | − | 1.28317i | ||||
\(963\) | 15.0711 | − | 31.5563i | 0.485658 | − | 1.01689i | ||||
\(964\) | − | 107.740i | − | 3.47008i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 25.3137 | − | 4.34315i | 0.814455 | − | 0.139738i | ||||
\(967\) | −1.61522 | + | 1.61522i | −0.0519421 | + | 0.0519421i | −0.732601 | − | 0.680659i | \(-0.761694\pi\) |
0.680659 | + | 0.732601i | \(0.261694\pi\) | |||||||
\(968\) | −3.12132 | + | 3.12132i | −0.100323 | + | 0.100323i | ||||
\(969\) | 19.3137 | − | 3.31371i | 0.620446 | − | 0.106452i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.0000i | − | 0.641831i | −0.947108 | − | 0.320915i | \(-0.896010\pi\) | ||
0.947108 | − | 0.320915i | \(-0.103990\pi\) | |||||||
\(972\) | −3.82843 | − | 59.5563i | −0.122797 | − | 1.91027i | ||||
\(973\) | 3.71573 | + | 3.71573i | 0.119121 | + | 0.119121i | ||||
\(974\) | −46.8701 | −1.50181 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.4558 | −1.00688 | ||||||||
\(977\) | 24.1127 | + | 24.1127i | 0.771434 | + | 0.771434i | 0.978357 | − | 0.206924i | \(-0.0663451\pi\) |
−0.206924 | + | 0.978357i | \(0.566345\pi\) | |||||||
\(978\) | −21.8995 | + | 30.9706i | −0.700269 | + | 0.990329i | ||||
\(979\) | 1.65685i | 0.0529533i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.9706 | − | 8.82843i | 0.797249 | − | 0.281870i | ||||
\(982\) | −34.1421 | + | 34.1421i | −1.08952 | + | 1.08952i | ||||
\(983\) | −1.72792 | + | 1.72792i | −0.0551122 | + | 0.0551122i | −0.734126 | − | 0.679014i | \(-0.762408\pi\) |
0.679014 | + | 0.734126i | \(0.262408\pi\) | |||||||
\(984\) | 4.72792 | + | 27.5563i | 0.150721 | + | 0.878464i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 46.6274i | − | 1.48492i | ||||||
\(987\) | 2.05887 | + | 1.45584i | 0.0655347 | + | 0.0463400i | ||||
\(988\) | 21.6569 | + | 21.6569i | 0.688996 | + | 0.688996i | ||||
\(989\) | −86.4264 | −2.74820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.1716 | 0.609005 | 0.304503 | − | 0.952512i | \(-0.401510\pi\) | ||||
0.304503 | + | 0.952512i | \(0.401510\pi\) | |||||||
\(992\) | 9.89949 | + | 9.89949i | 0.314309 | + | 0.314309i | ||||
\(993\) | 14.8284 | + | 10.4853i | 0.470566 | + | 0.332740i | ||||
\(994\) | − | 28.9706i | − | 0.918890i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.04163 | + | 46.8701i | 0.254809 | + | 1.48513i | ||||
\(997\) | 36.7696 | − | 36.7696i | 1.16450 | − | 1.16450i | 0.181025 | − | 0.983479i | \(-0.442059\pi\) |
0.983479 | − | 0.181025i | \(-0.0579415\pi\) | |||||||
\(998\) | 32.7279 | − | 32.7279i | 1.03598 | − | 1.03598i | ||||
\(999\) | 20.8995 | + | 37.3848i | 0.661231 | + | 1.18280i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 825.2.k.c.518.1 | 4 | ||
3.2 | odd | 2 | 825.2.k.f.518.2 | 4 | |||
5.2 | odd | 4 | 825.2.k.f.782.2 | 4 | |||
5.3 | odd | 4 | 165.2.k.a.122.1 | yes | 4 | ||
5.4 | even | 2 | 165.2.k.b.23.2 | yes | 4 | ||
15.2 | even | 4 | inner | 825.2.k.c.782.1 | 4 | ||
15.8 | even | 4 | 165.2.k.b.122.2 | yes | 4 | ||
15.14 | odd | 2 | 165.2.k.a.23.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.k.a.23.1 | ✓ | 4 | 15.14 | odd | 2 | ||
165.2.k.a.122.1 | yes | 4 | 5.3 | odd | 4 | ||
165.2.k.b.23.2 | yes | 4 | 5.4 | even | 2 | ||
165.2.k.b.122.2 | yes | 4 | 15.8 | even | 4 | ||
825.2.k.c.518.1 | 4 | 1.1 | even | 1 | trivial | ||
825.2.k.c.782.1 | 4 | 15.2 | even | 4 | inner | ||
825.2.k.f.518.2 | 4 | 3.2 | odd | 2 | |||
825.2.k.f.782.2 | 4 | 5.2 | odd | 4 |